Answer:
The measure of angle ABC is 36° ⇒ 1st answer
Step-by-step explanation:
Let us revise some important facts in the circle
The measure of the center angle is equal to the measure of its subtended arc
The measure of the inscribed angle is equal to half the measure of the central angle subtended by the same arc
The vertex of a central angle is the center of the circle and its sides are radii in the circle
The vertex of an inscribed angle is a point on the circle, and its sides are chords in the circle
In circle D
∵ D is the center of the circle
∵ A and C lie on the circle
- DA and DC are radii
∴ ∠ADC is a central angle subtended by arc AC
∴ m∠ADC = m of arc AC
∵ m∠ADC = (7x + 2)°
∵ m of arc AC = (8x - 8)°
- Equate them to find x
∴ 8x - 8 = 7x + 2
- subtract 7x from both sides
∴ x - 8 = 2
- Add 8 to both sides
∴ x = 10
Substitute the value of x in the measure of ∠ADC
∵ m∠ADC = 7(10) + 2 = 70 + 2
∴ m∠ADC = 72°
∵ AB and BC are two chords in circle D
∴ ∠ABC is an inscribed angle subtended by arc AC
∵ ∠ADC is a central angle subtended by arc AC
- By using the 2nd fact above
∴ m∠ABC = m∠ADC
∴ m∠ABC = × 72
∴ m∠ABC = 36°
The measure of angle ABC is 36 degrees
Circle geometry
To get the required measure of m<ABC, we will use the theorem that states that the measure of the central angle is equal to the measure of its subtended arc and;
The vertex of a central angle is the center of the circle and its sides are radii in the circle
According to the given circle D
∠ADC is a central angle subtended by arc AC
m∠ADC = m of arc AC
m∠ADC = (7x + 2)°
m of arc AC = (8x - 8)°
Equate to find the value of x
8x - 8 = 7x + 2
x - 8 = 2
x = 10
Substitute the value of x in the measure of ∠ADC
m∠ADC = 7(10) + 2 = 70 + 2
m∠ADC = 72°
∠ADC is a central angle subtended by arc AC
m∠ABC = 0.5 × 72
m∠ABC = 36°
Hence the measure of angle ABC is 36 degrees
Learn more on circle geometry here: https://brainly.com/question/24375372
the product of twice a number and one less than that same number
Answer:
(2n)*(n-1)
Step-by-step explanation:
What is the number that is 1 number before infinity?
WHOEVER WILL ANSWER FIRST AND CORRECT WILL BE THE BRAINLIEST and take ur time I am asking for fun to see who is the best☺
Answer:
напиши по русский
Я НЕ ПОНИМАЮ.
x-4 in word form
Please help it’s due today!
Answer:
x minus four
Step-by-step explanation:
Central Angles and Arc Measures Practice
What is X?
Answer: [tex]5^{\circ}[/tex]
Step-by-step explanation:
Given
[tex]\angle DIE=(18x-2)^{\circ}\\\angle DIH=15^{\circ}\\\angle FIG=103^{\circ}[/tex]
from the figure
[tex]\angle HIE=\angle GIF\quad [\text{vertically opposite angles}]\\\angle HID+\angle DIE=\angle GIF\\15^{\circ}+(18x)^{\circ}-2^{\circ}=103^{\circ}\\(18x)^{\circ}=103^{\circ}-13^{\circ}\\\\x=\dfrac{90^{\circ}}{18}\\\\x=5^{\circ}[/tex]
What is the sum of 0.5 and 0.3 ?
Answer:
0.8
Step-by-step explanation:
5 x 3 = 8 (Add the "0." at the end) That's all, hope it helped!
Answer:
The answer is 0.8. Think of it like a normal number.
can someone help me... thanks ❤️
Answer:
13m
Step-by-step explanation:
A drawer contains 2 Red Socks, 7 White Socks, and 9 blue sock Without looking, you draw out a sock and then draw out a second sock without returning the first sock. What is the probability that the first sock and the second sock are both red?
Answer:
1/153
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one ids attached to the event. If it doesn't a value of zero is attached to the event.
probability that the first sock and the second sock are both red = (number of red socks /total number of socks) x (number of red socks /total number of socks)
At the first pick, the probability = 2/18
At the second pick because there is no replacement, there would be 1 red socks and 17 socks = 1/17
2/18 x 1/17 = 1/153
Simplify: [tex]\frac{\left(x^{\frac{5}{2}}\cdot 6y^2\cdot \sqrt[3]{y^4}\right)}{12x^{\frac{1}{2}}\cdot \sqrt[4]{x^3}}[/tex]
Answer:
[tex]\frac{1}{2} x^{\frac{5}{4} }y^{\frac{10}{3}}[/tex]Step-by-step explanation:
[tex]\frac{x^{\frac{5}{2} }*6y^2*\sqrt[3]{y^4} }{12x^{\frac{1}{2}}*\sqrt[4]{x^3} } =[/tex] [tex]\frac{x^{ \frac{5}{2} }6y^2y^{ \frac{4}{3} } }{12x^{ \frac{1}{2} }x^{ \frac{3}{4} }} =[/tex][tex]\frac{1}{2} x^{\frac{5}{2} - \frac{1}{2} - \frac{3}{4}}y^{2+\frac{4}{3}}=[/tex][tex]\frac{1}{2} x^{\frac{5}{4} }y^{\frac{10}{3}}[/tex]What is 80% of 72 ? pls help due today
Answer:
Step-by-step explanation:
57.6
Answer:
57.6
Step-by-step explanation:
You multiply 72 by .8 because you have to change the percent into a decimal place to multiply it by. 0.8 is 80 hundredths and fractions are numbers out of 100. I hope I could help you :)
Can someone help me with this?
Answer:
Step-by-step explanation:
We first need to figure out how much money Jackie has since Pilar has the same amount of money, but in different coins. Jackie has 24 dimes and 13 quarters, so the amount of money is $2.40 + $3.25 = $5.65; therefore, Pilar has $5.65 also. In order to determine how many nickels and quarters Pilar has, we have to have a system of equations. It's up to us to write the equations we need to solve this. The first equation has to do with the NUMBER of coins Pilar has, the second has to do with the VALUE of each coin. We know that Pilar has only nickels and quarters and that she has a total of 53 coins. So the NUMBER equation is
n + q = 53
The VALUE equation relates how much each coin is worth to the total amount of money it equals:
.05n + .25q = 5.65.
Go back to the first equation and solve it for either n or q. I solved it for n:
n = 53 - q
Plug this into the second equation in place of n now to get:
.05(53 - q) + .25q = 5.65 and
2.65- .05q + .25q = 5.65 and
.20q = 3 so
q = 15. This means that there are 15 quarters. If there are 15 quarters, then there are
n + 15 = 53 nickels and
n = 38 nickels.
Can anyone answer this ASAP
Answer:
650 ft^2
Step-by-step explanation:
Without the gap, the area of the rectangle is 20ft x 35ft = 750 ft^2. The gap is a square having 10ft on the side so its area is 10ft x 10ft = 100 ft^2. Subtracting the area of the square gap from the rectangle gives you 650 ft^2.
Plz help fast will mark brainliest!!!
PLEASEEE HELP MEEEE
NO LINKSSS
Answer:
[tex]\huge\boxed{(2,\ 3);\ (-1,\ 6)}[/tex]
Step-by-step explanation:
[tex]f(x)=x^2-2x+3\to y=x^2-2x+3\\f(x)=-x+5\to y=-x+5\\\\\left\{\begin{array}{ccc}y=x^2-2x+3&(1)\\y=-x+5&(2)\end{array}\right[/tex]
substitute (1) to (2):
[tex]x^2-2x+3=-x+5[/tex] add x to both sides
[tex]x^2-2x+x+3=-x+x+5[/tex]
[tex]x^2-x+3=5[/tex] subtract 5 from both sides
[tex]x^2-x+3-5=5-5[/tex]
[tex]x^2-x-2=0\\\\x^2+x-2x-2=0\\\\x(x+1)-2(x+1)=0\\\\(x+1)(x-2)=0\iff x+1=0\ \vee\ x-2=0\\\\\boxed{x=-1\ \vee\ x=2}[/tex]
substitute the values of x to (2):
[tex]x=-1\\\\y=-(-1)+5=1+5=6\\\\\huge\boxed{(-1,\ 6)}\\\\x=2\\\\y=-2+5=3\\\\\huge\boxed{(2,\ 3)}[/tex]
Among the licensed drivers in the same age group, what is the probability that a 78-year-old was involved in an accident? Use the table below.
Answer:
C. 6.6%
Step-by-step explanation:
The probability of an event 'A' occurring, P(A) is given by the ratio of the number of times event A occurs to the some of all possible events
Mathematically, we have;
[tex]The \ probability \ of \ an \ event = \dfrac{The \ number \ of \ the \ required \ outcome}{The \ number \ of \ all \ possible \ outcomes}[/tex]
The number of drivers involved in an accident who are above 75 years = 13,321
The total number of drivers in accidents = (10,034 + 17,173+ 35,712+ 40,322 + 40,937 + 30,355 + 17,246 + 13,321) = 205,100
A 78-year-old is in the age group of 75 and older
∴ The probability that a 78-year-old licensed driver was involved in an accident = The probability that a 75 and older year-old licensed driver was involved in an accident = 13,321/205,100 ≈ 0.06495 = 6.5%
Therefore, the best option is option C. 6.6%
Answer:
4.2
Step-by-step explanation:
<333
please let me know if I did it good and lmk if I did anything wrong ( finding area )
What is the total area, in square meters, of the shaded sections of the trapezoid
below?
7 m
9.9 m
10 m
8.6 m
Answer:
84.5m would be the area
Step-by-step explanation:
7m, 10m = 35m
9.9m, 10m= 49.5m
35m + 49.5m+ 84.5m
Determine a simplified expression to represent the area of shaded region within the figure below
Answer:
[tex](5x-3)^{2}[/tex] - (3x+1)(2x-1)
Step-by-step explanation:
Determine the area of the large square: (5x - 3)(5x - 3)
Determine the area of the small rectangle: (3x + 1)(2x -1)
Subtract the area of the small rectangle from the area of the large square to get the area of the shaded region.
helpppppp meeeeeeeee
Answer:
True
Step-by-step explanation:
This is so basic haha but happy to help
help, don't guess. tyyyy
Answer:
[tex]\huge{\textbf{\textsf{{\color{skyblue}{An}}{\blue{sw}}{\red{er}}{\color{red}{:}}}}}[/tex]
0 (zero)
Step-by-step explanation:
The 8-sided die has numbers less than 9. So, they can never be greater than 9.
prove that the sum of two consecutive exponents of the number 5 is divisible by 30. If N ia the smaller of two consecutive exponents, then the sum of two consecutive exponents of 5 is equal to _ *30, and therefore is divisible by 30.
Answer:
5^n-1
Step-by-step explanation:
5^n-1*30
I just need a explanation pls
Answer:
SCreenshoit
wont lddlwd
Step-by-step explanation:
PLEASE HELP. NO SCAMMERS
the storm trooper camp is open for 7 and 1/2 hours a day. The camp keeps one guard on duty at a time, and their shift is 1 and 1/2 hours long. how many shifts are there a day?
Answer:
there are 5 shirts a day
Step-by-step explanation:
you divide the number of hours the camp is open by the time a guard is on duty. 7.5 ÷ 1.5 =5
A cyclist travels 5.8 km in 30 minutes.
What is his average speed in km/h?
Answer:
11.6km/hr
Step-by-step explanation:
You need to double 30 minutes to get an hour, so do the same with the distance.
5.8*2=11.6 km
11.6km/hr
How DISGUISE WILL BE WRITTEN IN THE CODE
Answer:
what are you asking?
Step-by-step explanation:
You've taken out a load for $5,000 for five years. The interest you'll be paying over the five years is $2,250. What interest rate are you paying?
i need someone to please explain to me STEP BY STEP how to do this thank you
Answer:
2
Step-by-step explanation:
divide 5,000 by 2,250 and you get 2 its like you have 0 quarters and you want to know how many you need to have to get 50 cent 50 divided by 25 equal 2 but your quistion answer is 2
Select all expressions that are equivalent to
2x + 5(–4x + 10) - (x + 4).
Show your work in the sketch pad that supports your
answer.
(Select all that apply.)
27x + 54
-19x + 46
2x - 30x + 50 - x - 4
2x + 30x + 50 - x +4
2x + 5(–4x + 10) - (x + 4).
-4+10=14
x+4=5-9
2x+5=7x
7+9=18
18-14=4
4 is your answer
help please!! like asap
Big points if you answer this
Answer:
i think its A but im not 100 percnt sure
Answer:
a
Step-by-step explanation:
In rectangle MNOP, MO = 4x - 10 and NP = 2x + 4.
What is the length of a diagonal?
Answer:
18
Step-by-step explanation:
From the rectangle, M O = NP
4x - 10 = 2x+4
4x-2x = 4 + 10
2x = 14
x = 14/2
x = 7
SInce MO and NP are the diagonal
Length of diagonal = 4x- 10
Length of diagonal = 4(7) - 10
Length of diagonal = 28 - 10
Length of diagonal = 18
hence the required length is 18
John is trying to convert an area from meters squared to millimeters squared. He multiplied the area he had by
1,000 and got the wrong answer. What should he have multiplied the original area by?
A) 100
B) 1,000
C) 1,000,000
D) 10
Answer:
1,000,000
Hope this helps <3